Nonlinear problems with asymmetric principal part

Abstract

The boundary value problem  is considered provided that f : [0, +∞) → [0, +∞) is Lipschitzian and  is continuous and Lipschitzian in xand x′. We assume that f is bounded by two linear functions kx and lx, where k > l > 0, and h is bounded. We find the conditions on (λ, µ) which guarantee the existence of a solution to the problem. These conditions are of geometrical nature.